Could you please elaborate?
1. The rules of go are very simple. (Well, kinda. Use, say, the Tromp-Taylor ruleset.)
2. The resulting game is very subtle, in e.g. the following senses. (a) For any game, define an "increment" to be how much better you need to be than someone else in order to beat them 75% of the time. Then the number of increments between a total beginner and God is larger for go than for any other game I know of. (b) Same as (a), but this time define an "increment" to be how much better you can get with a week's hard work or something. -- That is, there's a lot to learn, and learning it really makes you appreciably better at the game.
3. The difficulty of the game isn't simply a matter of getting better at mechanical calculations: there's a whole lot of strategy and "good taste" and so on.
4. It seems to be an uncommonly beautiful game. Now, any good game is going to have some aesthetic appeal for its expert players. But it seems as if (a) really good go players get more out of it aesthetically than, say, really good chess players get out of chess, and (b) one starts seeing aesthetic value in the game earlier in the process of getting better than with most other games.
5. (This is, I think, mostly a consequence of #1.) It's a very flexible game: you can use a different size of board (changing how long a game takes and the tactics/strategy balance), or give one player a handicap (changing the balance between the two) while keeping the game substantially the same. This is convenient practically, and (for reasons I can't currently articulate) it seems to me that it indicates something deeper about the game: it's a kind of Platonic essence that can be instantiated in many different ways. (I wonder occasionally about playing go on a graph that isn't just a square grid. It seems like hexagonal go wouldn't be too big a stretch, whereas to make a decent hexagonal chess game you have to change lots and lots of things.)
6. (Related to #1, #4 and #5.) It's a game that can be played with enjoyment even by total beginners: it's much more approachable than chess, for instance.
7. Although there's a lot to learn about the game, the understanding:brute-facts ratio in what you need to learn is better than in, say, chess. You can play go very well while knowing scarcely any detailed opening theory, whereas to be any good at chess you need to learn a lot of lines.
By the way, one of the reasons I "like" Go (in a purely objective, looking from a distance without learning it kinda way) is that, from what I've heard, even average players can beat computers at the game. Obviously, this is mostly to do with accidental, mechanical facts about number of possible moves, but in an age where Chess has been "won" by computers, it is something of an appeal for me. Do actual Go players feel the same way?
Computer moves always looked unnatural to me, though, and you could often exploit this easily. I'd say most players are at least comforted by lack of computer headway into Go.
How about playing on a Penrose tessellation generated within some bounds, like a square or circle.
Come to think of it, I wonder what Conway's Life would look like if it were shoehorned onto such a graph. I'm not sure how one would define the neighborhood, but sounds interesting to explore.
(Be cautious about believing anything I say too much. I'm a pretty weak player.)
Go has a kind of deceptive shallowness. The rules are extremely simple[0]. You can see 90% of what’s going on on a given board in a few seconds. (The board looks like a simplified illustration of something else – like the phase portrait of an uglier game.) Another beginner and I can play a game that looks roughly like a game between masters, and with a heavy enough handicap we can even play a satisfying game with them.
What’s fascinating and addictive is that there’s no big secret. Learning go, for me, is reminding myself that it’s simpler than it looks. All I have to do is surround territory. It’s very, very hard. The last 10% of understanding a board takes decades.
0. The Tromp-Taylor rules, which you mentioned and serve as an excellent introduction for the curious hacker, are at http://homepages.cwi.nl/~tromp/go.html . Notice the 150-line Haskell version.